Precision Measurement of the Proton Elastic Cross

Section at High Q2

W. Bertozzi, S. Gilad (spokesperson), J. Huang,B. Moffit (spokesperson) † , P. Monaghan, N. Muangma, A. Puckett,

X. Zhan

Massachusetts Institute of Technology, Cambridge, MA, USA

A. Camsonne, J. P. Chen, E. Chudakov, C. W. de Jager, J. Gomez,J.-O. Hansen, D. W. Higinbotham, M. Jones, J. LeRose, R. Michaels,

A. Saha, V. Sulkosky, B. Wojtsekhowski (spokesperson)

Thomas Jefferson National Accelerator Facility, Newport News, VA, USA

J. Arrington (spokesperson), D. F. Geesaman, K. Hafidi, R. Holt,P. E. Reimer, P. Solvignon

Argonne National Laboratory, Argonne, Illinois, USA

A. Radyushkin

Old Dominion University, Norfolk, VA, USAThomas Jefferson National Accelerator Facility, Newport News, VA, USA

S. Abrahamyan, S. Mayilyan, A. Shahinyan

Yerevan Physics Institute, Yerevan, Armenia

D. Day, R. Lindgren, N. Liyanage, V. Nelyubin, B. E. Norum, K. Paschke

University of Virginia, Charlottesville, VA, USA

W. Boeglin, P. Markowitz, J. Reinhold

Florida International University, Miami, FL, USA

D. Armstrong, T. Averett, R. Feuerbach, M. Finn, L. Pentchev,C. Perdrisat

College of William and Mary, Williamsburg, VA, USA

† contact person: Bryan Moffit (moffit@jlab.org)

Jefferson Lab PAC32 Proposal 20 June 2007

J. Annand, D. Ireland, R. Kaiser, K. Livingston, I. MacGregor,G. Rosner, B. Seitz

University of Glasgow, Glasgow, Scotland, UK

T. Holmstrom

Randolph-Macon College, Ashland, VA, USA

J. Calarco

University of New Hampshire, Durham, NH, USA

Y. Qiang

Duke University, Durham, NC, USA

G. Huber

University of Regina, Regina, Saskatchewan, Canada

K. A. Aniol, D. Margaziotis

California State University, Los Angeles, Los Angeles, California, USA

C. E. Hyde

Old Dominion University, Norfolk, VA, USALaboratoire de Physique Corpusculaire, Universite Blaise Pascal, Aubiere, France

B. Anderson, R. Subedi

Kent State University, Kent, OH, USA

and The Hall A Collaboration

Abstract

Using the base experimental equipment for Hall A, and beam energies of 6.6, 8.8, and 11 GeV,we propose to measure the proton elastic cross section to a statistical precision of better than 1%over a Q2 range of 7–17.5 GeV2. A few items of general purpose instrumentation are proposedto ensure that the total uncertainty will be below 2%. The resulting measurement will providemeans for extracting the proton’s magnetic form factor and be the benchmark for future crosssection measurements at high Q2. The experiment requests a total of 31 days for data taking,commissioning, and calibration. The experiment could be ready to run as soon as the highenergy beam is available, and would be well suited to commissioning the upgraded beamlineinstrumentation for Hall A.

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Contents

1 Collaboration Contributions to 12 GeV Baseline Equipment 5

2 Introduction 6

2.1 Physics Overview 6

2.2 Overview 6

2.3 pQCD Mechanism 7

2.4 Handbag Mechanism 8

2.5 Additional Remarks 8

2.6 Summary of Physics Goals 8

2.7 Background - Previous Measurements 9

2.8 Motivation for the Current Proposal 10

2.9 Factors Contributing to Accuracy of the Experimental Results 13

3 Proposed Experiment 15

3.1 Detailed Kinematics for the Measurement 15

3.2 Experimental Setup 16

3.3 Requested Beam Time 20

4 Systematic Uncertainties 21

4.1 Incident Energy 21

4.2 Scattering Angle 21

4.3 Incident Beam Angle 21

4.4 Beam Charge 22

4.5 Target Density 22

4.6 Radiative Corrections 22

4.7 Optics and Spectrometer Acceptance 24

4.8 Detector Efficiencies and CPU/Electronic Dead Time 25

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4.9 Endcap Subtraction 25

4.10 π− Background 26

4.11 Total Systematic Uncertainty 26

5 Summary 27

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1 Collaboration Contributions to 12 GeV Baseline Equipment

There are four items listed under the Hall A 12 GeV baseline equipment:

• Arc energy measurement system• the Compton polarimeter,• the Moller polarimeter,• the HRS readout electronics.

This collaboration intends to make major contributions to the readout electronics upgradeof HRS. In this project we plan to contribute in development of the software and hardwareas well as in commissioning of electronics in beam. The members of the University ofVirginia group are already involved in the present upgrade of the Compton polarimeter.As stated in previous 12 GeV PAC proposals, this involvement will continue into upgradingand commissioning of the Compton polarimeter for the high energy beam.

The collaboration intends to make major contributions in design and commissioning ofthe equipment for arc energy measurement system and the Moller polarimeter.

MIT will commit 1 FTE-year (1 postdoc and 1 graduate student) to the field measurementsof the upgraded dipole magnets for use in the arc energy measurements.

In addition to the 12 GeV baseline equipment, this collaboration intends to make majorcontributions for the additional general purpose instrumentation and analysis techniquesmentioned in this proposal. We note that these items may also be commissioned and usedfor the 6 GeV program. This collaboration has the expertise and resources to implementthese proposed improvements.

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2 Introduction

Nucleon electromagnetic form factors have provided significant information on the struc-ture of the nucleon, been used to test predictions of pQCD, and provide one of the cor-nerstones of GPD modeling. Existing data at high Q2 have large uncertainties (statisticaland systematic), and also have large unknown uncertainties related to two-photon ex-change (TPE) corrections and the contribution from Gp

E. This limits the ability to extractinformation on the Q2 dependence, as well as introduction uncertainty in the knowledgeof the elastic e–p cross sections at JLab kinematics. As the uncertainty on the e–p crosssection yields a correlated uncertainty on measurements of Gp

E, GnM , and even Gn

E, as wellas uncertainty in experiments that rely on a knowledge of the elastic cross section such asquasielastic A(e,e’p) measurements. The proposed measurements will provide both higherprecision measurements of the cross section, and reduced dependence on uncertaintiesrelated to TPE and Gp

E.

The recent understanding of GpE/Gp

M indicates that the extraction of GpM from SLAC

measurements has significant corrections that were not taken into account, and whichmodify both the overall size and Q2 dependence of Gp

M . While future understanding of thehigh Q2 behavior of Gp

E/GpM and two-photon exchange can be used to improve extraction

from the SLAC data, the proposed measurements has three main advantages over theexisting SLAC data. First, we will significantly improve the statistical and systematicuncertainties on the cross section measurements. Second, because the measurement isat lower ε, the contributions from Gp

E are significantly smaller than for the large Q2

SLAC data (where GpE may be negative and large). Third, while there is still significant

uncertainty in the two-photon exchange corrections at large Q2, this contributes to theuncertainty in extracting Gp

M , but does not increase the uncertainty in determining thee–p elastic cross section values needed by other high-Q2 measurements at JLab. The SLACdata, taken at significantly higher beam energies, would have to be extrapolated down tolower ε values to be used as input for JLab measurements, and this extrapolation would beaffected by the uncertainty in the two-photon exchange corrections. We will be measuringthe cross sections at kinematics where any TPE corrections will be very similar to whatis seen in other experiments at JLab.

2.1 Physics Overview

2.2 Overview

In view of the remarks in the Introduction, we consider several interesting issues thatmotivate us to explore further the measurement of e− p elastic cross section at JLab:

(1) While the form factor deviates significantly from the dipole fit, it is not clear to whatextend it is consistent (or inconsistent) with pQCD scaling.

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(2) What is the power of the Q2 dependence as a function of momentum, and how doesthe form factor approach the pQCD limit?

(3) What information can be learned about the GPDs constrained by new precisionmeasurements of the cross section?

(4) Is it possible to distinguish the VDM mechanism from direct coupling of the virtualphoton to a single quark?

In order to present a framework for addressing these issues, we next present discussionsof reaction mechanisms in the pQCD and GPD approaches.

2.3 pQCD Mechanism

The traditional framework for the interpretation of hard exclusive reactions has been per-turbative QCD (pQCD) [1]. This is based in part on the observation that the onset of scal-ing in Deep Inelastic Scattering (DIS) occurs at the relative low scale of Q2 ∼ 1− 2 GeV2,thereby giving rise to expectations that pQCD might also be applicable to the exclusiveprocesses in the range of a few GeV2. In the pQCD approach to the FFs, the three valencequarks are active participants in the hard subprocess, which is mediated by the exchangeof two hard gluons. The soft physics is contained in the so-called valence quark distributionamplitudes. The pQCD mechanism leads naturally to the so-called constituent countingrules for exclusive processes.

Indeed, the observation that many exclusive reactions, such as elastic electron scattering,pion photoproduction, and RCS, approximately obey scaling laws has led some to believethat the pQCD mechanism dominates at experimentally accessible energies. There seemsto be little theoretical disagreement that the pQCD mechanism dominates at sufficientlyhigh energies; however, there is no consensus on how high is “sufficiently high.” Indeed,despite the observed scaling, absolute cross sections calculated using the pQCD frameworkare very often low compared to existing experimental data, sometimes by more than anorder of magnitude. Moreover, several recent JLab experiments that measure polarizationobservables also disagree with the predictions of pQCD. In the Gp

E experiments [2, 3]the slow falloff of the Pauli form factor F2(Q

2) up to Q2 of 5.6 GeV2 provides directevidence that hadron helicity is not conserved, contrary to predictions of pQCD. This hasbeen interpreted in terms of logarithmic corrections to the leading order pQCD behavior,coming from angular momentum of the quarks [4]. However, reproducing the lower Q2

data where polarization measurements of GpE/Gp

M exist requires an unreasonably largevalue of ΛQCD [5]. Measurements of Gp

E at higher Q2, combined with the higher precisionmeasurements of Gp

M proposed here, will allow for a more detailed examination of thelogarithmic corrections, as well as providing a consistency check on these corrections.

Similar findings were made in the π0 photoproduction experiment [6], where both the non-zero transverse and normal components of polarization of the recoil proton are indicativeof hadron helicity-flip, which is again contrary to the predictions of pQCD.

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2.4 Handbag Mechanism

The handbag mechanism offers new possibilities for the interpretation of hard exclusivereactions. For example, it provides the framework for the interpretation of so-called deepexclusive reactions, which are reactions initiated by a high-Q2 virtual photon. The softphysics is contained in the wave function describing how the active quark couples to theproton. This coupling is described in terms of GPDs. The GPDs have been the subject ofintense experimental and theoretical activity in recent years [7, 8]. They represent “super-structures” of the proton, from which are derived other measurable structure functions,such as parton distribution functions (PDF) and form factors.

The nucleon form factors and the PDFs extracted from DIS are the only quantities whereone can directly probe specific values of the GPDs. They provide the cornerstones whenmodeling GPDs, and the only constraints at high Q2, and make it easier to interpret theresults of other measurements that are sensitive to moments of GPDs, or combinationsof GPDs. Having reliable knowledge of the GPDs in the regions where this is possible isimportant in maximizing what we can learn from the broader program of GPD studies.

2.5 Additional Remarks

It is important to realize that the issues posed at the start of this section are not limitedto the elastic e − p reaction. Indeed, they are questions that need to be addressed byall studies of the proton using exclusive reactions in the hard scattering regime. The oldparadigm for addressing these questions was the pQCD mechanism and the distributionamplitudes. It is quite likely that the new paradigm will be the handbag mechanism andGPDs. In any case, the reaction mechanism needs to be tested, not only over a wide rangeof kinematic variables but also over a wide range of different reactions. Elastic electronscattering at high momentum transfer offers the best possibility to test the mechanismfree of complications from additional hadrons.

2.6 Summary of Physics Goals

We propose measurements of the electron scattering from the proton at an incident elec-tron energy of 6.6, 8.8 and 11 GeV, at large scattering angles corresponding to Q2 range7 -17.5 GeV2. The specific physics goals are as follows:

(1) Provide a stringent test of the notion that the elastic F1 form factor exhibit pQCDlike scaling behavior at Q2 above 7-8 GeV2.

(2) Determine the form factor GpM with accuracy several times higher that it is known

from existing single data set obtained at SLAC.

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(3) Measure the cross section of e− p scattering at kinematics used in JLab experimentto allow accurate normalization for study of Gn

M and many others.

The overall precision with which we will address these physics goals will be discussed insection 3.

2.7 Background - Previous Measurements

Measurement of the proton’s elastic electromagnetic form factors has been of consider-able interest to the Jefferson Lab experimental program and is critical for describing theproton’s underlying structure.

In terms of the Sachs electromagnetic form factors, the differential cross section for elasticep scattering is written compactly as

dσ

dΩ= σmott

ε(GpE)2 + τ(Gp

M)2

ε(1 + τ), (1)

where the structure-less cross section σmott is given by

σmott =

(α

2E

cos θ2

sin2 θ2

)2E ′

E, (2)

with τ = Q2/4M2p , and ε = [1 + 2(1 + τ) tan2(θ/2)]−1.

These form factors have been extracted in Rosenbluth Separation experiments via elas-tic scattering using either traditional inclusive p(e, e′)p measurements [9–14], or elasticp(e, p)e′ [15]. In addition, polarization transfer measurements [3, 16] have dramaticallyimproved the extraction of Gp

E at large Q2.

These recent polarization transfer measurements have generated much excitement in thenuclear physics community, showing a large discrepancy in the measurement of the ra-tio of the electric form factor to the magnetic form factor, Gp

E/GpM , compared to that

measured by the other methods. The current explanation of this discrepancy is the ap-plication of radiative corrections at leading order to extract the ratio. These correctionscan vary significantly with ε. Of considerable interest at present has been the inclusionof the full two-photon exchange contributions to these corrections. A few reviews of thecurrent understanding from an experimental and theoretical point of view are found inRef. [5, 17–19].

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]2 [GeV2Q0 10 20 30

DG

pµ/p M

G

0.8

1.0

AndivahisBartelBerger

JanssensLittSillWalkerThis Proposal

Fig. 1. Published world data for GpM/µpGD as a function of Q2 (Refs. [9–14, 20]). Uncertainties

shown do not include the effect of the normalization uncertainty, which is 3% on the Sill et al.cross sections, and projected to be 1–1.2% for the proposed measurements.

2.8 Motivation for the Current Proposal

As shown in Figure 1, a majority of the Q2 coverage for GpM is for Q2 < 8 GeV2. The best

data above 8 GeV2 is the Sill et al., measurement from SLAC [20]. The cross section uncer-tainties on the Sill measurement vary from 4% at Q2 = 5 GeV2, to 8% for Q2 ≈ 20 GeV2,not including an overall normalization uncertainty of 3%. An earlier measurement [21] alsomeasured elastic scattering in this Q2 range, but had much larger uncertainties (5–30%,with a normalization uncertainty of approx. 5%).

The extraction of GpM from this data was performed assuming scaling, i.e. Gp

E = GpM/µp.

This assumption had GpE contribute 6% (2%) to the cross section at Q2 = 5 GeV2

(20 GeV2). From the recent polarization transfer measurements, we now know that thecontribution from Gp

E is significantly less for the Q2 values where GpE/Gp

M has been mea-sured. The true contribution from Gp

E will be zero near Q2 ≈ 6–7 GeV2, increase as Q2

increases, where GpE/Gp

M becomes negative and increases in magnitude with Q2. If the lin-ear behavior seen in the polarization measurements [3] continues, |µpG

pE/Gp

M | will becomegreater than one above Q2 ≈ 13 GeV2, and the contribution from Gp

E will actually belarger than was assumed in the previous analyses. Thus, instead of the contribution fromGp

E decreasing by 4% between Q2 of 5 and 15–20 GeV2, it will increase by 4%, yielding a

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noticeably modified Q2 dependence for GpM .

In addition, two-photon exchange (TPE) effects also yield a correction to the extractedvalue of Gp

M . Except for the IR-divergent terms, these contributions were completelyneglected in the analysis of all previous measurements. Therefore, while the cross sectionsare measured at the 5–10% level, the uncertainty in Gp

M is larger than was assumed inprevious extractions, and difficult to determine.

Future measurements of GpE/Gp

M at large Q2 can be used to improve the extraction ofGp

M from the SLAC data, and help correct for the artificial Q2 dependence introducedby the assumption of form factor scaling. However, the uncertainties on the high Q2

SLAC data are fairly large, and the contributions from GpE will be significant, because

the measurements are all at large ε. For example the contribution from GpE, assuming the

linear behavior observed in polarization transfer measurements continues, would implya 4% correction to the cross section data around 18 GeV2, while for the measurementsproposed here and taken at lower ε values, the contribution would be only 1–2%. Whilethe 12 GeV upgrade will extend direct measurements of Gp

E/GpM to higher Q2, we will

only have direct measurements over some of the Q2 range, and the reduced sensitivity toGp

E will allow for a cleaner extraction of GpM .

The uncertainty in the two-photon exchange corrections at these high Q2 yield an addi-tional uncertainty in the extraction of Gp

M . These corrections are somewhat larger for themeasurements proposed here than for the SLAC measurements. However, for the SLACmeasurements, the TPE corrections also make it difficult to reliably extrapolate the SLACcross section measurements to the JLab kinematics since they were taken at higher beamenergy and thus lower ε. As discussed below, the elastic e–p cross section is an importantinput to several other experiments, and so even with the larger TPE corrections, it ismore reliable to use the measurements proposed here, at similar energies to other futureJLab measurements, than to try and extrapolate the SLAC cross section measurements.

The measurements proposed here will allow for better extractions of both the proton’smagnetic form factor and the elastic e–p cross section. In addition, it will provide betterconstraints on the high-Q2 behavior of the form factors, and thus allow for stronger testsof models of the nucleon form factor. This will be of particular importance as otherJLab measurements improve the Q2 coverage of the other electromagnetic form factors.These measurements will also provide the highest Q2 constraints on Generalized PartonDistributions (GPDs) from exclusive reactions. Only the DIS measurements of the partondistribution functions can provide information on the GPDs at higher Q2 values, and theQ2 dependence of these is well understood.

Figure 2 shows the precision with which we can test the prediction of a 1/Q4 behavior forGp

M . The red points are the power as taken by comparing pairs of GpM measurements from

Sill [20]. To have a reasonable measure of the Q2 dependence, one needs to look at thedata over a large Q2 range. The solid red line shows the power taken from using all of theSill data, and the dashed lines show the uncertainty, if we assume that there is no change

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Fig. 2. The power, n, on a 1/Qn fit to individual pairs of GpM points. The red points are from

the SLAC data, while the blue points are for the proposed measurements (offset to show the Q2

separation of the points). The curves are described in the text.

in the falloff of the form factor as we go to higher Q2. If we try to look for a change in thisbehavior with Q2, e.g. by fitting these extractions to a straight line, we obtain the blackdotted line. Clearly, we cannot use these data to study the approach to scaling, or to makea precision determiniation of the Q2 dependence except by integrating over the entire Q2

range. The blue points show what can be done with the proposed measurements, usingevery other point (i.e. a typical spacing of 2 GeV2 for each extraction). As you can see,each point does a better job of determining the power of the Q2 falloff better than thecombined result from all of the Sill data above 7 GeV2, allowing both a better measure,and a measure of the approach to the expected perturbative behavior.

In addition to studying GpM by itself, these data will provide precision measurements on

the elastic e–p cross section. All of the other electromagnetic form factor measurements aretaken relative to either Gp

M or the elastic e–p cross section. Polarization transfer measure-ments in e–p scattering provide only the ratio of Gp

E/GpM , and one needs the cross section

to obtain the absolute values for the individual form factors. Measurements of GnM rely on

either the ratio of neutron to proton QE scattering on the deuteron (D(e, e′n)/D(e, e′p))or the asymmetry in scattering from polarized Helium-3. In both cases, one is measuringthe ratio of the elastic e–n cross section to the elastic e–p cross section, and so the un-certainty in σe−p translates into an error on σe−n and thus Gn

M and GnE, which is again

measured as a ratio to GnM . Thus, the error in the e − p elastic cross section can yield a

significant and highly correlated error in all of the electromagnetic form factors. Such acorrelated error in all of the measurements could be an important limiting factor in using

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these measurements to constrain models of the nucleon structure.

The best previous cross section measurements in this range have uncertainties at the 5–10% level. In addition, because these are taken at smaller scattering angles (and higherenergies), the extrapolation to JLab kinematics for the same Q2 values also relies onour knowledge of Gp

E and TPE at these very large Q2 values. Therefore there will beadditional poorly known uncertainties in the value, and possibly the Q2 dependence, ofthe cross section. This will translate into uncertainties of all of the nucleon electromagneticform factors, as well as other high Q2 measurements of elastic or quasielastic scattering.

To achieve these goals, we propose the measurement of the proton’s elastic cross sectionfrom a range in Q2 from 7–17.5 GeV2 using the existing High Resolution Spectrometersof Hall A. With a relatively short amount of time (31 days) and a few additional piecesof general purpose instrumentation a high precision would be obtained. Thus creatinga precision benchmark for high Q2 cross section measurements for future experiments.As the contribution of Gp

E to the cross section is expected to be negligible for muchof this Q2 range, and small for all Q2 values, this measurement will provide a precisedetermination of the evolution of Gp

M at high Q2.

The proposed measurements will improve the precision on the cross section measurementsfrom 5–10% down to below 2%. Because they are measured at kinematics appropriate forother JLab 12 GeV measurements, there will be minimal additional theoretical uncer-tainty in extrapolating to the kinematics of other JLab measurements. In addition, thesemeasurements will be at smaller ε values than the SLAC measurements, yielding smallercorrections from Gp

E, even at the largest Q2 values where they may well be larger thanassumed in the analysis where form factor scaling was assumed. We also include two Q2

points that will be measured at each of two different beam energies. This will not beused to perform a Rosenbluth separation, but will provide measurements of Gp

M at threedifferent epsilon values to test the corrections due to Gp

E and two-photon exchange. Thepoint at lower ε will have an extremely small contribution from Gp

E, even if GpE is quite

large, but somewhat larger TPE corrections. The higher ε point will be somewhat moresensitive to the value of Gp

E, but have a significantly smaller TPE correction.

2.9 Factors Contributing to Accuracy of the Experimental Results

A measurement of the elastic cross section to this precision is quite an undertaking, assystematic factors must be understood to an unprecedented level. We plan to aggressivelyreduce the uncertainties in these factors that contribute to the accuracy of the experimen-tal results:

• Incident beam energy and it’s stability,• Electron scattering angles and the mapping of the spectrometer focal plane variables

to the target variables,• Spectrometer acceptance with an extended target,

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• Target density the stability of the luminosity under experimental conditions.• Radiative corrections.

Our plan to address these factors, include the following:

• Absolute determination of the beam energy with the eP method and upgraded arc.Beam energy stability monitored with Tiefenback energy,

• Construction and commissioning of the Precision Angle Measurement (PAM) deviceand installation of an additional VDC in each spectrometer focal plane,

• Utilization of the PAM micro-strip detector (MSD) that will be made to be slightlylarger than and placed in front of the spectrometer collimator. Several solid carbontargets with 1-2 cm spacings along the incident beam direction for measure of theacceptance as a function of the target length,

• Use of the Hall A luminosity monitor to measure the frequency spectrum of targetdensity fluctuations and monitor the stability of the experimental luminosity throughoutthe entire run.

• Standard radiative corrections (not including TPE) are well know and are understoodto the 0.5% level. TPE corrections have gone through a great deal of progress a shouldbe better know by the time of the running of the experiment. A few kinematic pointsare also proposed to measure the ε dependence of the elastic cross section, which hasbeen shown to be correlated with the TPE corrections.

These items will be explained in more detail in the following sections.

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3 Proposed Experiment

We propose to measure the proton elastic cross section and use these data to extractGp

M over the Q2 range of 7–17.5 GeV2. At beam energies of 6.6 GeV, 8.8 GeV, and 11 GeV,both Hall A High Resolution spectrometers (HRSs) will be primarily in a symmetricconfiguration in electron detector mode to double the counting statistics and provide ameans for additional systematic checks. The technical details of the HRSs can be foundin Ref. [22]. A beam current of 80 µA combined with a 20 cm target with a density of4.3× 1022 protons/cm3 (0.072 g/cm3) provides a luminosity of about 4.3× 1038 cm−2s−1

allowing the proton elastic cross section to be measured in only 31 days (including allcommissioning and overhead).

We begin this section by showing the specific kinematics for this measurement, followedby a detailed description of the experimental setup. Finally, we provide a summary of therequested beam time to complete the measurement.

3.1 Detailed Kinematics for the Measurement

Ee Q2 θe E′ ε Rate Time Events(GeV) (GeV)2 (deg) (GeV) (Hz) (hours)

6.6 7.0 35.4 2.869 0.62 7.45 0.7 40k6.6 8.0 42.0 2.351 0.51 2.29 2.4 40k6.6 9.0 52.0 1.782 0.37 0.48 11.6 40k6.6 10.0 67.0 1.249 0.23 0.15 38.3 40k8.8 9.0 29.3 4.000∗ 0.67 3.38 3.3 40k8.8 10.0 33.3 3.465∗ 0.59 1.31 8.5 40k8.8 11.0 38.0 2.945 0.51 0.53 10.5 40k8.8 12.0 44.0 2.423 0.41 0.21 26.7 40k8.8 13.0 53.0 1.859 0.30 0.06 67.4 28k

11.0 13.0 31.3 4.065∗ 0.58 0.36 21.2 28k11.0 14.0 35.0 3.525∗ 0.50 0.17 39.0 24k11.0 15.5 42.0 2.742 0.39 0.05 52.8 20k11.0 17.5 58.0 1.689 0.21 0.01 271.4 16k

517.8Table 1Kinematics for the proposed measurement. Calculated rates assume a luminosity of 4.3 ×1038 cm−2s−1, solid angle coverage of 5.4 msr, and proton form factor parametrization fromRef. [23]. Kinematics with scattered electron energy (E′) with an asterisk (*) indicate measure-ments that will only be done with the Left HRS. The total time is slightly less than the sumof the individual times because the Right HRS will take data on the higher Q2 points for thekinematics where only the Left arm can reach the required momentum.

The kinematics for the proposed experiment are shown in Table 1. Each Q2 point hasbeen optimized to achieve a statistical precision in the proton elastic cross section of 0.5-0.8%. Three Q2 points at 9, 10 and 13 GeV2 are repeated to check for systematics arising

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from the change in beam energy from 6.6 GeV to 8.8 GeV and 8.8 GeV to 11 GeV.The ε dependence to the cross section is expected to be weak at this high Q2 (due toτ(Gp

M)2/ε(GpE)2 ' 35). Four Q2 points involve scattered electron energies (E ′) that are

beyond the current capabilities of the Right HRS. Therefore, these points will measuredusing only the Left HRS.

3.2 Experimental Setup

3.2.1 The Targets

We plan to use the standard Hall A cryogenic target ladder, composed of a liquid hydro-gen target and Carbon and Aluminum solid targets for optics calibrations and backgrounddeterminations. We plan to use the 20 cm LH2 racetrack cells that feature vertical cryo-genic fluid flow to reduce the effects of target density fluctuations. These target cells havebeen successfully used in previous high luminosity Hall A experiments. Background fromquasielastic scattering from the aluminum windows will be evaluated with aluminum foilsused to simulate the contribution. The optics targets (with 1-2 cm spacing along zlab) willbe used to optimize the spectrometer matrix elements using an improved method similarto the one current used and outlined in Ref. [24]. This method is discussed in a latersection. We will also take some runs at the lower Q2 values on a 4cm hydrogen target, asa test of the normalization and target length acceptance corrections.

3.2.2 The Spectrometer setup

The proposed measurement will use both High Resolution Spectrometers (HRSs) in elec-tron detection mode. Each detector package, shown in Figure 3 will consist of:

• A set of three Vertical Drift Chambers (VDC) for tracking.• A pair of trigger scintillator planes (S0 and S2m).• Gas Cherenkov counter for pion rejection and trigger.• A lead glass calorimeter for addition pion rejection and trigger.

We plan to augment the pair of VDCs, currently present in each spectrometer arm, withan additional and identical VDC to reduce systematics of track reconstruction efficiency.Hall A currently has a spare VDC readily available, and the components and electronicsrequired to build a second chamber is on-site. To have them installed, the first scintillatortrigger plane (S1) will need to be removed. The S0 scintillator plane will be installed toprovide high trigger efficiency.

The main trigger, to cleanly select electron events, will be the coincidence signal betweenthe Gas Cherenkov and S2m scintillator plane. Singles from S2m, as well as a set ofrandom pulsers (generated from a small scintillator in a black box with a radioactivesource), will serve as auxiliary triggers to check the efficiency of the main trigger. The

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VDC

GasCherenkov

S2m Total AbsorptionShower

Counters

pre ShowerCounters

Cen

tral

Ray

S0

Fig. 3. Schematic of detector package for the HRSs.

lead glass calorimeter (pre-shower and shower detectors) signals will serve as a powerfulinstrument for background suppression. Two secondary triggers, the coincidence of S0 andthe Gas Cherenkov, and the coincidence of S0 and S2m, will also be used. This will allowfor continuous measurement of the S2m and Cherenkov trigger efficiencies.

3.2.3 Beam Energy Measurement

To measure the incident beam energy, this experiment will use the upgraded Arc methodand eP systems. These methods have shown the capability of providing a precision of≤ 3 × 10−4 [22] and show good agreement with each other. Both methods will requireupgrade to be used after the 12 GeV upgrade [25]. The eP system will require a minorupgrade to its electron trigger to allow it to function at larger beam energies.

The beam energy spread will be monitored constantly using the Synchrotron Light In-terferometer (SLI) that was commissioned and used during E94-107 (showing that theaccelerator was able to achieve a beam energy spread as small as 6×10−5 (FWHM) [26]).We plan to use the OTR and the Tiefenback Energy as a cross check to monitor the beamenergy stability.

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3.2.4 Beam Intensity and Luminosity Monitoring

The beam intensity will be monitored using the two RF cavity monitors located justupstream of the raster, along with the newer cavity monitors (that also measure position)that are located just upstream of the target. This original system has worked successfullyfor 10 years, and provides a measure of the beam current to ≤0.5% [22]. To accuratelynormalize the elastic cross section, a beam calibration will need to be performed and weplan to include the signal from the cavity monitors for each event in the data acquisition(along with the normal scaler readout system).

Monitoring of the stability of the target density will be provided by the Hall A luminositymonitor. This system also provides the capability of determining the frequency spectrumof density fluctuations induced by local beam heating. A scaler-based, integrating dataacquisition system will be constructed to allow for the detector signals from this monitorto be inserted into the data stream allowing for the constant monitoring of the targetdensity over the entire run.

3.2.5 Incoming beam and scattering angle

OTR

HRS

beam line

Wire Scanner 2

BPM2 BPM1

Slot for target mounting

Micro Strip Detector Slot for MSD mounting

Wire Scanner 1

Scattered electron

Precision Angle Measurement

Thick Al frameTungsten Wire Target

Fig. 4. Schematic of Precision Angle Measurement (PAM) device as presented in Ref. [27]. Notethat only one MSD and Spectrometer are pictured, where this proposed experiment will requirethe use of two of each.

Apart from the strip line beam position monitors, just upstream of the target location, aPrecision Angle Measurement (PAM) device will allow for improved accuracy and greaterreliability in determining the incoming beam angle as well as the electron scattering angle.

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A rough schematic of PAM is shown in Figure 4, as it was presented in [27]. The mainfeatures of this devices include:

• Two wire scanners to monitor the beam position up and downstream of the target,• A vertically installed 10 µm tungsten wire target to define the center of the target

ladder,• A silicon micro-strip detector (MSD) in front of each spectrometer (slightly larger than

the acceptance defining collimator) to detect scattered charged particles before theyenter the spectrometer. These MSDs will be of the same design as that shown in Figure 5.

All of these are mounted on to a aluminum frame. Slots for the MSD, within the frame,will allow for the movement of the MSD for variety spectrometer angles. The originaldesign incorporated the entire frame within the scattering chamber, but may be easilyadapted for use outside of the chamber.

Fig. 5. Schematic and picture of the micro-strip detector (MSD) designed for the CMS experimentat the LHC. The intermediate electronic board design is currently being discussed for JLab use.

With the tungsten wire target and MSD installed, the scattering angle would be measuredby the spectrometer and MSD to the level of 0.05 mrad (or better). This measurementwould also serve to measure the acceptance and optical properties of the spectrometer.Measurement of the incoming beam angle will be measured by the wire scanners which canthen be used to calibrate the cavity and stripline beam position monitors just upstreamof the target. In addition, PAM will allow for improved optics studies of the spectrometer,improving our knowledge of the optics and acceptance, and thus allowing for a betterabsolute uncertainty in the cross section measurements.

The simplicity of the design of this apparatus, is such that it may be designed and commis-sioned for experiments requiring precision angle measurements before the 12 GeV energyupgrade.

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3.3 Requested Beam Time

To complete the precision measurement of the proton elastic cross section for a range inQ2 of 7–17.5 GeV2, we request 31 days. Table 2 provides a breakdown of how this time isallocated.

Item HoursProduction on LH2 518Background from Aluminum Foils 91Optics calibrations and angle measurements (PAM) 80eP and Arc Energy Measurements 12Target density measurements/tests 8Data on 4cm LH2 targets 8BCM calibration 8Beam energy changes 8Checkout/calibration 12Total 745

Table 2Detailed beam time request.

A large fraction of the beam time requested is for production data taking at the highestQ2 point (17.5 GeV2). We note that this data may also be taken with a single spectrometerin parallel (or parasitically) to the running of the 12 GeV Polarization Transfer experiment(proposed for this PAC) [28] if it is also approved.

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4 Systematic Uncertainties

We plan to be aggressive in minimizing the systematic uncertainties so that the statis-tical precision of the proposed measurement is not undermined. It is our assertion thatthis goal is realized by the inclusion of a small amount of general purpose items to theHall A baseline equipment, and improved analysis techniques. In this section, we discussthe systematics that are expected to contribute to the point to point and normalizationuncertainties.

4.1 Incident Energy

Calibration of the absolute energy will be done using the eP and Arc method. At present,these methods provide an absolute precision of (3–4)×10−4. Stability of the beam energycentral value can be monitored based on the BPMs in the Hall A arc, and both the absoluteenergy and energy drifts can be verified using the elastic peak position. Assuming thatthe eP precision is still (3–4)×10−4 for the higher energy beams, the resulting uncertaintyon the cross-section measure is below ±0.3% for all kinematics.

4.2 Scattering Angle

Measurement of the central scattering angle of the spectrometers is typically be providedby direct survey and usually provides a precision of better than ±0.2 mrad. This yields across section uncertainty of less than 0.3%. However, on several occassions a discrepancyhas been found to be up to several mrad [29]. Without another independent measurement,this error would not have been found. For this reason, a separate absolute angle measure-ment must be made by some version of the PAM device. With this device, discussed in theprevious section, we expect to better the precision of the measurement to be improved byat least a factor of two, and to provide a more reliable measurement of the spectrometerpointing.

4.3 Incident Beam Angle

The incident beam angle is currently determined utilizing the stripline Beam PositionMonitors (BPMs) that are calibrated to provide an absolute position of the beam throughuse of wire scanners (superharps). The current implementation of this method providesan uncertainty of 0.1 mrad [22]. This corresponds to an uncertainty contribution of lessthan ±0.2% in the cross section, which can be further reduced using the PAM device.

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4.4 Beam Charge

With careful monitoring and calibration of the beam current monitors, the beam chargeis typically to known to ±0.5% or better, as long as the beam current is large enoughthat uncertainties in the BCM offsets for zero current are not small. This is typicallyonly an issue for currents below 10 µA. For the proposed measurements, we will run at80 µA, and will have a fixed beam current for all of the main data taking. Under thesecircumstances, the uncertainty is largely in the absolute normalization, and the drifts overtime are smaller [15]. We assume a 0.3% point-to-point normalization, and a 0.4% scaleuncertainty.

4.5 Target Density

The 20 cm racetrack cells have provided Hall A with reduced density fluctuations com-pared to the cigar-shaped cells (whose performance is detailed in Refs. [30, 31]). Althoughthere is no current detailed literature showing the racetrack cell performance, we make aneducated guess that they are equivalent or better than the tuna-can shaped cells (whichalso feature a vertical cryogenic flow). These cells were shown to contribute a 0.5% system-atic error to previous measurements. We plan to perform a detailed study of the densityfluctuations from the racetrack cell before or during the commissioning of this experiment.The standard procedure to characterize beam-related target density fluctuations is to takedata as a function of beam current, and compare the normalized yield as a function ofbeam current. We will take beam current scans for both high rate and low rate kinematics,to ensure that we do not mistake density fluctuations for deadtime, efficiency, multipletrack corrections, or other rate-dependent effects. We will also take beam current scans ona solid target, to provide a calibration for the case with no density fluctuations. This hasallowed for precise measurements of the current-dependent density fluctuations, which aresmall and very nearly linear with current for the transverse flow target designs.

4.6 Radiative Corrections

The radiative corrections are significant at these Q2 values, and the approximations some-times used at lower energies begin to be less reliable. The prescriptions used for elasticscattering have been studied in this Q2 range [32, 33], and the standard radiative correc-tions, shown in Figure 6 (a-d), (not including two-photon exchange) are understood atthe 0.5% level.

Most previous experiments quoted uncertainties that were dominated by two-photon ex-change (TPE) corrections (shown in Figure 6 (e,f)), where were assumed to be at the1-1.5% level. In fact, it now appears that these corrections may be at the several percentlevel and are at this time still quite uncertain at these kinematics. There is a great deal

22

Fig. 6. Feynman diagrams for Born Approximation and radiative corrections (a-h) for elec-tron-proton scattering.

of progress on the calculation of these corrections, and several experiments underway tohelp extract TPE in order to verify the calculations. We have three kinematics where weextract Gp

M at multiple ε values, which will also provide a test of the calculated TPEcorrections (when combined with future measurements of Gp

E).

However, in many cases, the TPE uncertainties are not relevant. For other measurementsmade at the same Q2 and beam energy, the TPE corrections are identical, and the uncer-tainty involved in separating Gp

M from TPE corrections does not affect the uncertainty inthe total cross section. So experiments such as the measurement of the neutron magneticform factor, which measures the ratio of e–n to e–p elastic cross sections, and quasielas-tic scattering measurement at high Q2 simply need the e–p cross section, and are notaffected by the uncertainty in TPE. Therefore, we do not include an uncertainty fromTPE in the extracted cross sections, although it will yield an additional uncertainty inthe extraction of Gp

M . Given our present understanding of TPE corrections, this wouldyield an uncertainty of ∼2% on the extraction of Gp

M , based on a rough estimate of themodel-dependence of current calculations [33, 34]. This will of course be reduced as ourunderstanding of the TPE corrections improves.

.

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4.7 Optics and Spectrometer Acceptance

The current procedures used to determine the spectrometer acceptance typically results ina systematic error in the cross section of about 2%. The uncertainty is smaller for elasticscattering, because the elastic peak populates only the central region of the momentumacceptance, and because one integrates over the peak, making the result less sensitive tothe accuracy of the momentum reconstruction.

The largest issues are the loss of events at apertures within that magnetic elements, andthe target length acceptance. We will perform careful studies of the optics and acceptanceof the spectrometer, taking data with optics target, thin foils spaced 1-2 cm apart, usingboth sieve slits and using the PAM device to determine the angles of the events. Inaddition, we will use a collimator that is slightly narrower, approximately 5.4 cm comparedto the standard 6.3 cm opening. With this collimator, far fewer events are lost insidethe spectrometer magnets (mainly on the sides of the dipole), making the target lengthacceptance much flatter, and easier to model. We will take measurements on a 4 cm cell forsome of the lower Q2 settings at a few different angles, to verify the normalization of theacceptance corrections for the longer targets. With careful modeling of the spectrometer,the uncertainty in the acceptance of the spectrometer (for elastic scattering from a 4cmcell) can be known to 1% [35]. With the careful optics studies and additional informationprovided by the PAM, we hope to do this well or better for the extended targets.

φ tg

θ tg

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

-0.02 0 0.02

Fig. 7. Schematic of a sieve slit (left) and reconstructed events to the target in-plane and out--of-plane angles (right) as presented in Ref. [22]. Horizontal and vertical lines in the right plot,indicate the predicted locations of the reconstructed holes.

We also intend to improve the current optics optimization analysis code that was first

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developed based on a χ2-minimization of scattered events through a sieve-slit placed atthe entrance to the spectrometer, shown in Figure 7. This analysis has proven to work wellusing low beam energy on a carbon foil where tight cuts in reconstructed δ are made onthe elastic peak to help remove sieve punch through events. This analysis is more difficultat larger beam energy and scattering angle due to the fall of the 12C elastic cross section.In this case, quasi-elastic scattering from 12C can be used but does not cleanly removepunch-through events. This leads to a background distribution, that is not necessarily flat,that causes systematic shifts of the reconstructed sieve pattern from the χ2-minimizationroutine.

To improve this analysis method at high beam energies a set of routines to performa “peak”-search will be included. This procedure would entail finding maximum peakheights in focal plane distributions and locating their cooresponding peaks in the sieveplane. The χ2-minimization technique would then use this information in conjunctionwith using the typical cuts on events that appear to be within the vicinity of a sieve hole(which are subject to non-uniform background distributions).

4.8 Detector Efficiencies and CPU/Electronic Dead Time

Detector efficiencies for the HRS are generally high with relatively small uncertainties.Because our rates are always low, corrections due to multiple tracks and electronic deadtime, which tend to be more difficult to correct precisely, should be very small. The thirdVDC installed in each arm will also serve to reduce the systematics associated with thetrack reconstruction efficiency. Computer dead time should also be very small, althoughthis correction is well understood even for high rates. We will have multiple triggers, toallow for constant monitoring of the detector efficiencies. This should allow us to achievean overall uncertainty to the cross section to about ±0.5%, which we take to be roughlyequal parts point-to-point and scale contributions.

4.9 Endcap Subtraction

Dummy target runs will be taken to measure the contribution from the Aluminum endcapsof the cryotarget. The contribution from the endcaps will be approximately 5% or less,and the main uncertainty in the subtraction comes from knowing the relative Aluminumthicknesses of the target walls and the dummy target (which we plan to measure by meansof X-ray attenuation to the 1% level), and the difference in radiative corrections for thereal target and the dummy. We will be able to verify the normalization by comparingdata in the superelastic region for all settings. The uncertainty in the endcap subtractionshould be known to a few percent of the size of the subtraction, or about 0.1-0.2%. Weassume a 0.1% scale, and 0.1% point-to-point uncertainty.

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4.10 π− Background

The π− rates within the spectrometer acceptance have been calculated based on fits toSLAC data [36]. This calculation is the same as that typically used for inclusive π− pho-tonproduction and is understood to be accurate to within a factor of two. We estimate theratio of π−/e rates to be in the range of 2–200 within the δ region of interest (integratingfrom the elastic peak to the pion threshold) for the proposed kinematic points. This resultis quite acceptable given the online (using the Gas Cherenkov as a trigger) and offlineanalysis (using the lead glass calorimeters) pion rejection factor that is typically obtainedin Hall A of at least 104 with an electron detection efficiency of 99.5% [37].

4.11 Total Systematic Uncertainty

Contributions to the uncertainty are summarized in Table 3.

Source ∆σ/σ (%)Point to point uncertainties

Incident Energy <0.3Scattering Angle 0.1–0.3Incident Beam Angle 0.1–0.2Radiative Corrections* 0.3Beam Charge 0.3Target Density Fluctuations 0.2Spectrometer Acceptance 0.4–0.8Endcap Subtraction 0.1Detector efficiencies and dead time 0.3

Sum in quadrature 0.8–1.1Normalization uncertainties

Beam Charge 0.4Target Thickness/Density 0.5Radiative Corrections* 0.4Spectrometer Acceptance 0.6–1.0Endcap Subtraction 0.1Detector efficiencies and dead time 0.4

Sum in quadrature 1.0–1.3Statistics 0.5–0.8

Total (Scale+Rand.+Stat.) 1.2–1.7* Not including TPE; see subsection 4.6

Table 3Expected systematic uncertainties in dσ/dΩ. The lower numbers indicate the values we hope toachieve if the new PAM device functions as well as desired.

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5 Summary

In conclusion, we proposed to measure the proton elastic cross section in the Q2 range of7–17.5 GeV2 to a statistical precision of less than 1%. Understanding of systematic contri-bution will be aided by a few additional general purpose instrumentation for the baselineHall A equipment and the improvement of the current analysis techniques. Measurementsof form factors whose analysis requires an accurate proton cross section will greatly benefitfrom the precision of this measurement. Also, extraction of Gp

M from this measurementwill provide a means for accurate determination of Gp

E from future polarization transfermeasurements.

We request 31 days to successfully complete the experiment.

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